The correct options are
A increases
B decreases
Metals are the elements that have the tendency to lose electrons, i.e. they are electron donors. So, metallic character means the tendency to easily lose electrons.
Down a group:
Atomic size increases and the nuclear pull on the valence electron reduces. As a result, electron can be easily pulled out from the valence shell. Hence, metallic character increases down a group.
Across a period:
Atomic size decreases and nuclear pull on the valence electrons increases. As a result, electron cannot be easily pulled out from the valence shell. Hence, metallic character decreases across a period.